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MnO2 + KNO3 + K2CO3 = CO2 + K2MnO4 + KNO2

Input interpretation

MnO_2 manganese dioxide + KNO_3 potassium nitrate + K_2CO_3 pearl ash ⟶ CO_2 carbon dioxide + K_2MnO_4 potassium manganate + KNO_2 potassium nitrite
MnO_2 manganese dioxide + KNO_3 potassium nitrate + K_2CO_3 pearl ash ⟶ CO_2 carbon dioxide + K_2MnO_4 potassium manganate + KNO_2 potassium nitrite

Balanced equation

Balance the chemical equation algebraically: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 KNO_3 + c_3 K_2CO_3 ⟶ c_4 CO_2 + c_5 K_2MnO_4 + c_6 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, K, N and C: Mn: | c_1 = c_5 O: | 2 c_1 + 3 c_2 + 3 c_3 = 2 c_4 + 4 c_5 + 2 c_6 K: | c_2 + 2 c_3 = 2 c_5 + c_6 N: | c_2 = c_6 C: | c_3 = c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: |   | MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2
Balance the chemical equation algebraically: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 KNO_3 + c_3 K_2CO_3 ⟶ c_4 CO_2 + c_5 K_2MnO_4 + c_6 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, K, N and C: Mn: | c_1 = c_5 O: | 2 c_1 + 3 c_2 + 3 c_3 = 2 c_4 + 4 c_5 + 2 c_6 K: | c_2 + 2 c_3 = 2 c_5 + c_6 N: | c_2 = c_6 C: | c_3 = c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2

Structures

 + + ⟶ + +
+ + ⟶ + +

Names

manganese dioxide + potassium nitrate + pearl ash ⟶ carbon dioxide + potassium manganate + potassium nitrite
manganese dioxide + potassium nitrate + pearl ash ⟶ carbon dioxide + potassium manganate + potassium nitrite

Equilibrium constant

Construct the equilibrium constant, K, expression for: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MnO_2 | 1 | -1 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CO_2 | 1 | 1 K_2MnO_4 | 1 | 1 KNO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 1 | -1 | ([MnO2])^(-1) KNO_3 | 1 | -1 | ([KNO3])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) CO_2 | 1 | 1 | [CO2] K_2MnO_4 | 1 | 1 | [K2MnO4] KNO_2 | 1 | 1 | [KNO2] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: |   | K_c = ([MnO2])^(-1) ([KNO3])^(-1) ([K2CO3])^(-1) [CO2] [K2MnO4] [KNO2] = ([CO2] [K2MnO4] [KNO2])/([MnO2] [KNO3] [K2CO3])
Construct the equilibrium constant, K, expression for: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MnO_2 | 1 | -1 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CO_2 | 1 | 1 K_2MnO_4 | 1 | 1 KNO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 1 | -1 | ([MnO2])^(-1) KNO_3 | 1 | -1 | ([KNO3])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) CO_2 | 1 | 1 | [CO2] K_2MnO_4 | 1 | 1 | [K2MnO4] KNO_2 | 1 | 1 | [KNO2] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([MnO2])^(-1) ([KNO3])^(-1) ([K2CO3])^(-1) [CO2] [K2MnO4] [KNO2] = ([CO2] [K2MnO4] [KNO2])/([MnO2] [KNO3] [K2CO3])

Rate of reaction

Construct the rate of reaction expression for: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MnO_2 | 1 | -1 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CO_2 | 1 | 1 K_2MnO_4 | 1 | 1 KNO_2 | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) KNO_3 | 1 | -1 | -(Δ[KNO3])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2MnO_4 | 1 | 1 | (Δ[K2MnO4])/(Δt) KNO_2 | 1 | 1 | (Δ[KNO2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: |   | rate = -(Δ[MnO2])/(Δt) = -(Δ[KNO3])/(Δt) = -(Δ[K2CO3])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2MnO4])/(Δt) = (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: MnO_2 + KNO_3 + K_2CO_3 ⟶ CO_2 + K_2MnO_4 + KNO_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MnO_2 | 1 | -1 KNO_3 | 1 | -1 K_2CO_3 | 1 | -1 CO_2 | 1 | 1 K_2MnO_4 | 1 | 1 KNO_2 | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) KNO_3 | 1 | -1 | -(Δ[KNO3])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) K_2MnO_4 | 1 | 1 | (Δ[K2MnO4])/(Δt) KNO_2 | 1 | 1 | (Δ[KNO2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -(Δ[MnO2])/(Δt) = -(Δ[KNO3])/(Δt) = -(Δ[K2CO3])/(Δt) = (Δ[CO2])/(Δt) = (Δ[K2MnO4])/(Δt) = (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

 | manganese dioxide | potassium nitrate | pearl ash | carbon dioxide | potassium manganate | potassium nitrite formula | MnO_2 | KNO_3 | K_2CO_3 | CO_2 | K_2MnO_4 | KNO_2 Hill formula | MnO_2 | KNO_3 | CK_2O_3 | CO_2 | K_2MnO_4 | KNO_2 name | manganese dioxide | potassium nitrate | pearl ash | carbon dioxide | potassium manganate | potassium nitrite IUPAC name | dioxomanganese | potassium nitrate | dipotassium carbonate | carbon dioxide | dipotassium dioxido-dioxomanganese | potassium nitrite
| manganese dioxide | potassium nitrate | pearl ash | carbon dioxide | potassium manganate | potassium nitrite formula | MnO_2 | KNO_3 | K_2CO_3 | CO_2 | K_2MnO_4 | KNO_2 Hill formula | MnO_2 | KNO_3 | CK_2O_3 | CO_2 | K_2MnO_4 | KNO_2 name | manganese dioxide | potassium nitrate | pearl ash | carbon dioxide | potassium manganate | potassium nitrite IUPAC name | dioxomanganese | potassium nitrate | dipotassium carbonate | carbon dioxide | dipotassium dioxido-dioxomanganese | potassium nitrite

Substance properties

 | manganese dioxide | potassium nitrate | pearl ash | carbon dioxide | potassium manganate | potassium nitrite molar mass | 86.936 g/mol | 101.1 g/mol | 138.2 g/mol | 44.009 g/mol | 197.13 g/mol | 85.103 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 535 °C | 334 °C | 891 °C | -56.56 °C (at triple point) | 190 °C | 350 °C boiling point | | | | -78.5 °C (at sublimation point) | |  density | 5.03 g/cm^3 | | 2.43 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | | 1.915 g/cm^3 solubility in water | insoluble | soluble | soluble | | decomposes |  dynamic viscosity | | | | 1.491×10^-5 Pa s (at 25 °C) | |  odor | | odorless | | odorless | |
| manganese dioxide | potassium nitrate | pearl ash | carbon dioxide | potassium manganate | potassium nitrite molar mass | 86.936 g/mol | 101.1 g/mol | 138.2 g/mol | 44.009 g/mol | 197.13 g/mol | 85.103 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 535 °C | 334 °C | 891 °C | -56.56 °C (at triple point) | 190 °C | 350 °C boiling point | | | | -78.5 °C (at sublimation point) | | density | 5.03 g/cm^3 | | 2.43 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | | 1.915 g/cm^3 solubility in water | insoluble | soluble | soluble | | decomposes | dynamic viscosity | | | | 1.491×10^-5 Pa s (at 25 °C) | | odor | | odorless | | odorless | |

Units